Question 860032
{{{(sin(x))/(1-cos(x)) + (1-cos(x))/(sin(x)) = 2csc(x)}}}


LHS 

{{{(sin(x))/(1-cos(x)) + (1-cos(x))/(sin(x))}}}
LCM of denominator

(1-cos(x)(sin(x))

we get {{{ (sin^2(x)+(1-cos(x))^2))}}}/{{{((1-cos(x))*(sin(x)))}}}


(sin^2(x)+1-2cos(x)+cos^2(x))/((1-cos(x)*sin(x))


(2-2cos(x))/((1-cos(x)*sin(x))

2(1-cos(x))/(1-cos(x)*sin(x))

=2/sin(x)

=2csc (x)

= RHS